Related papers: Multirate methods for ordinary differential equati…
Cell collective migration plays a crucial role in a variety of physiological processes. In this work, we propose the Runge-Kutta random feature method to solve the nonlinear and strongly coupled multiphase flow problems of cells, in which…
We are motivated to solve differential algebraic equations with new multi-stage and multisplitting methods. The multi-stage strategy of the waveform relaxation (WR) methods are given with outer and inner iterations. While the outer…
We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the…
We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an…
A weighted version of the parareal method for parallel-in-time computation of time dependent problems is presented. Linear stability analysis for a scalar weighing strategy shows that the new scheme may enjoy favorable stability properties…
Stabilized Runge-Kutta methods are especially efficient for the numerical solution of large systems of stiff nonlinear differential equations because they are fully explicit. For semi-discrete parabolic problems, for instance, stabilized…
Neural network-based methods for solving differential equations have been gaining traction. They work by improving the differential equation residuals of a neural network on a sample of points in each iteration. However, most of them employ…
When in a digital control strategy there are samples lost due to limitations, diff t multirate (MR) control options can be used for solving the problem: Dual-rate inferential control (IC) and model-based dual-rate control (MBDR). The…
The nonlinear gyrokinetic equations describe plasma turbulence in laboratory and astrophysical plasmas. To solve these equations, massively parallel codes have been developed and run on present-day supercomputers. This paper describes…
A unified theoretical framework is suggested to examine the energy dissipation properties at all stages of additive implicit-explicit Runge-Kutta (IERK) methods up to fourth-order accuracy for gradient flow problems. We construct some…
The Parareal algorithm is used to solve time-dependent problems considering multiple solvers that may work in parallel. The key feature is a initial rough approximation of the solution that is iteratively refined by the parallel solvers. We…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
This research presents a model of a complex dynamic object running on a multi-core system. Discretization and numerical integration for multibody models of vehicle rail elements in the vertical longitudinal plane fluctuations is considered.…
We propose a new probabilistic scheme which combines deep learning techniques with high order schemes for backward stochastic differential equations belonging to the class of Runge-Kutta methods to solve high-dimensional semi-linear…
We study existence and uniqueness of the fixed points solutions of a large class of non-linear variable discounted transfer operators associated to a sequential decision-making process. We establish regularity properties of these solutions,…
We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…
The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined…
In this work, we concern with the high order numerical methods for coupled forward-backward stochastic differential equations (FBSDEs). Based on the FBSDEs theory, we derive two reference ordinary differential equations (ODEs) from the…
The 4-th order Runge-Kutta method in the complex plane is proposed for numerically advancing the solutions of a system of first order differential equations in one external invariant satisfied by the master integrals related to a Feynman…